English

Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows

Fluid Dynamics 2021-09-13 v1 Soft Condensed Matter

Abstract

We consider the creeping flow of a Newtonian fluid in a hemispherical region. In a domain with spherical, or nearly spherical, geometry, the solution of Stokes equation can be expressed as a series of spherical harmonics. However, the original Lamb solution is not complete when the flow is restricted to a semi-infinite space. The general solution in hemispherical geometry is then constructed explicitly. As an application, we discuss the solutions of Marangoni flows due to a local source at the liquid-air interface.

Keywords

Cite

@article{arxiv.2109.04773,
  title  = {Stokes equation in a semi-infinite region: generalization of Lamb solution and applications to Marangoni flows},
  author = {G. Koleski and T. Bickel},
  journal= {arXiv preprint arXiv:2109.04773},
  year   = {2021}
}